# Options Pricing and the Greeks

### Intrinsic value of an option

Intrinsic value is the value of the option at expiration ie. the difference between spot price (S) and strike price (K). For put options, the payoff would be either K-S for an in-the-money situation or 0 for an out-of-the-money situation. For call options, the payoff would be either S-K for an in-the-money situation or 0 for an out-of-the-money situation.

### Time value of an option (also known as extrinsic value)

Time value is the difference between the market price of an option and its intrinsic price. Time value considers time to maturity, implied volatility, and rate of interest (rho). The longer the time to maturity, the more expensive an option price (and therefore a greater extrinsic value) since there is more time to be in-the-money. The more volatile the underlying is, the more expensive an option price (and therefore a greater extrinsic value) since there is a higher possibility for an option to be used when volatility hits a certain direction favourably. Lastly, the rate of interest is factored into the time value, but since the risk-free rate of interest doesn’t change very often, rho will normally only have a significant impact on longer-term options.

### Example of how intrinsic value and extrinsic value works

For example, if a call option has a strike price of $30 and the underlying stock is trading at $28, that option has an intrinsic value of $2. The actual option may have a market price of $5, so the extrinsic value is $3.

### The Greeks

The Greeks capture the sensitivity of an option’s price subject to the changes in its pricing formula input variables. The primary Greeks (delta, gamma, vega, theta, rho) are calculated as the first partial derivative of the options pricing model (for example, the Black-Scholes model). Delta, gamma, vega, and theta are the most common Greeks while rho is arguably the least important for the reason above. Nevertheless, we will discuss all five.